The numbers $ a_1, a_2, ... a_n $ are called a Diophantine n-tuple if $ a_ra_s + 1 $ is a perfect square whenever $ r \neq s $ . The whole subject started with Diophantus of Alexandria who found that the rational numbers $$ {1 \over 16},\ {33\over 16},\ {68\over 16},\ {105\over 16} $$
have this property. (You should check this for yourself). Fermat was the first person to find a Diophantine 4-tuple with whole numbers, namely $1$, $3$, $8$ and $120$. Even now no Diophantine 5-tuple with whole numbers is known.